Given Epsilon > 0, come up with a delta? Limit problem.

Limits have been introduced. So far my instructor has had us make tables to see what value x was approaching. Although I don't understand exactly how limits are EVALUATED (different from looking at a chart & saying "yeah, it looks like it's approaching 4 or whatever", it's pretty clear & makes intuitive sense.

Anyways, I've never seen a problem like this before.

Can someone please walk me through this. I have no idea where to start. The limit has already been solved...

You appear to be in an early stage of a mathematical analysis course: ##\forall \epsilon > 0 \ \ \ \exists \delta ... \ \ ## such that ... etc.

So it comes down to correct wording and putting the explicit definition to work explicitly.
For assistance with that, a literal rendering of the problem statement and of the relevant definition is useful (to say the least).

For that purpose we have a homework template, which might help you get started. I don't know if you've seen it come by ? (it's in bold face, so I suspect a yes here).